Gaur-gaurkoak
Ekitaldi eta jardunaldiak
Data: 2024(e)ko irailaren 25a 12:00
Seminario de Investigación: Nagata Dimensions and Lipschitz Extensions into Quasi-Banach Spaces
INAMAT2 organiza este seminario impartido por Jan Bima de la Charles University (Prague). Se celebrará el día 25 de septiembre de 2024 en la sala "Seminario 2" del Edificio de las Encinas.
ABSTRACT:
Given two metric spaces N and M in inclusion and 0<p< 1, we wish to determine the smallest constant tp(N,M) such that any Lipschitz map f:N->Z into any p-Banach space Z can be extended to a Lipschitz map f':M->Z satisfying Lip(f')< t_p(N,M).Lip(f).
In my talk, I will present a recent result showing that if N has finite Nagata dimension at most d with constant B, then tp(N,M) < B.(d+1)^{1/p -1}. \log (d+2)$ for all 0<p<1. I will show that examples of spaces with finite Nagata dimension include doubling spaces, as well as minor-excluded metric graphs. Interestingly, I will also establish that the constant tp(N,M) generally increases as p approaches zero